Knots and Links

by Dale Rolfsen

Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers "practical" training. After reading it, you will be able to do many compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements. It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included.

Genres: Mathematics, Nonfiction

439 pages, Paperback

First published December 1, 2003

Reviews

[Chris · Rating 5 out of 5]

It's definitive for good reason.

People who don't think mathematics is interesting should check the google preview of this book.

[Lulu]

Knot theory